Strange results from Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg16022] Strange results from Integrate*From*: Sergio Terrazas <sterraza at campus.cdj.itesm.mx>*Date*: Sat, 20 Feb 1999 02:52:08 -0500*Sender*: owner-wri-mathgroup at wolfram.com

Dear mathgroupers: I was working with a probability density function when I got the following strange result: f[x_]= Exp[-20 (x-12.5)] Integrate[f[x],{x,12.6,Infinity}] Out= 6.51852 x 10^92 =A1=A1What?!! NIntegrate[f[x],{x,12.6,Infinity}] Out= 0.135335 (Correct!) If I use exact numbers like 125/10 instead of 12.5, I get f[x_]= Exp[-20 (x-12.5)] (Note the 12.5) Integrate[f[x],{x,126/10,Infinity}] (Note the 126/10) Out= 0 ( ???) Now with both exact values: f[x_]= Exp[-20 (x-125/10)] (Note the 125/10) Integrate[f[x],{x,126/10,Infinity}] (Note the 126/10) Out= 1/E^2 (Correct!) Now using the fundamental theorem of calculus: (Using the definition of f with reals) f[x_]= Exp[-20 (x-12.5)] g[x_]=Integrate[f[x],x] Out= -E^(250-20x) (Correct) g[Infinity]-g[12.6] = 0.135335 What is going on? Is Integrate just unrelaiable with non exact numbers?? (Scary !!) I will appreciate any comments from the insiders. Thanks in advance ( Oh! by the way, I an using v. 3.0.1 for windows) Sergio Terrazas Juarez, Mexico